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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Ultimate Foundation of Truth
Date: Sun, 2 Mar 2025 16:01:09 -0600
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On 3/2/2025 3:25 PM, Richard Damon wrote:
> On 3/2/25 4:16 PM, olcott wrote:
>> On 3/2/2025 2:11 PM, dbush wrote:
>>> On 3/2/2025 3:01 PM, olcott wrote:
>>>> On 3/2/2025 1:27 PM, dbush wrote:
>>>>> On 3/2/2025 2:21 PM, olcott wrote:
>>>>>>
>>>>>> When formal systems can be defined in such a way that they are not
>>>>>> incomplete and undecidability cannot occur it is stupid to define
>>>>>> them differently.
>>>>>>
>>>>>
>>>>> That doesn't change the fact that Robinson arithmetic contains the 
>>>>> true statement "no number is equal to its successor" that has 
>>>>> *only* an infinite connection to the axioms
>>>>
>>>> If RA is f-cked up then toss it out on its ass.
>>>> We damn well know that no natural number is equal to its
>>>> successor as a matter of stipulation.
>>>
>>> We know it in RA though *only* an infinite connection to its axioms.
>>> Yet the system still exists, and the axioms of the system make that 
>>> statement true, but *only* though an infinite connection to its axioms.
>>>
>>>>
>>>> I have eliminated the necessity of systems that contain true 
>>>> statements that have *only* an infinite connection to their 
>>>> truthmakers. All
>>>> formal systems that can represent arithmetic do not
>>>> contain true statements that have *only* an infinite connection to 
>>>> their truthmakers unless you stupidly define them in a way that
>>>> makes them contain true statements that have *only* an infinite 
>>>> connection to their truthmakers.
>>>
>>> As it turns out, any system capable of expressing all of the 
>>> properties of natural numbers contain at least one true statement 
>>> that has *only* an infinite connection to its truthmakers.
>>>
>>> Note also that I took the liberty of replacing "incomplete" in your 
>>> above statement with the accepted definition to make it more clear to 
>>> all what's being discussed.
>>>
>>> So if you only allow systems where all true statements have a finite 
>>> connection to their truthmakers, then you don't have natural numbers.
>>>
>>> So choose: do you want to have natural numbers, or do you only want 
>>> systems where all true statements have a finite connection to their 
>>> truthmaker?
>>
>> Tarski's True(X) is implemented by determining a finite connection
>> to a truth-maker for every element of the set of human knowledge
>> and an infinite connection to a truth-maker for all unknowable truths.
>>
>>
> 
> Right, and thus is itself a proxy truth-maker for what it answer.
> 
> Thus given P := ~True(P)
> 
> If True determines that P has no connection to a truth maker, and thus 
> returns false, then P will be true, 

True(LP) determines that P is an infinite sequence,
aborts its evaluation of this infinite sequence
and returns false meaning not true stopping all
evaluation thus not feeding false back into the
evaluation sequence.

The self-contradictory part of LP is unreachable
in the same way as shown below.

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}

The self-contradictory part of DD emulated by HHH
is unreachable code.


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer